Simplify the following expression: $t = \dfrac{66y^3 - 55y^2}{-77y^2}$ You can assume $y \neq 0$.
Solution: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $66y^3 - 55y^2 = (2\cdot3\cdot11 \cdot y \cdot y \cdot y) - (5\cdot11 \cdot y \cdot y)$ The denominator can be factored: $-77y^2 = - (7\cdot11 \cdot y \cdot y)$ The greatest common factor of all the terms is $11y^2$ Factoring out $11y^2$ gives us: $t = \dfrac{(11y^2)(6y - 5)}{(11y^2)(-7)}$ Dividing both the numerator and denominator by $11y^2$ gives: $t = \dfrac{6y - 5}{-7}$